Question

A two-digt number is 3 more than 4 times the sum of its digit's. If 18 is added to
number. Its digits are reversed. find the number ​

Answer 1

Answer:

The number is 35. If you add 18 to the number it will reversed I.e. 53

Step-by-step explanation:

Let unit digit = x

Let ten's digit = y

Therefore number will be 10(y) + x

A. T. Q.

10y + x = 4(x+y) + 3

10y +x = 4x +4y +3

10y - 4y = 4x - x +3

6y = 3x +3

Y= (3x+3)/6..................... (eq 1)

If 18 is added to the number,

Unit digit will be y

Ten's digit will be x

New Number will be 10x +y

A. T. Q.

10Y + x +18 = 10x +y

10y - y +18 = 10x - x

9y + 18 = 9x

Taking 9 as a common, we get

Y + 2 = x

Putting y = (3x+3)/6 from eq 1

(3x+3)/6 + 2 = x

Multiplying whole equation by 6

3x+ 3 +12 = 6x

15 = 3x

5 = x

Thus

X= 5

Y= 3

The number is 35

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Answer 2

AnsWer :

35.

Solution :

• Let ten place be x
• and unit place be y.

Now,

Case 1.

1. A two- digits number is 3 more than 4 times the sum of it's digits number.

$\implies\tt10x + y = 4(x + y) + 3. \\ \implies\tt10x + y = 4x + 4y + 3. \\ \tt \implies6x - 3y = 3. \\ \tt \implies2x - y = 1. - - - (1)$

Case 2.

1. If 18 is added to the number it's digits are reversed.

$\tt \implies18 + 10x + y = 10y + x. \\ \tt \implies18 = 9y - 9x. \\ \tt \implies y - x = 2 - - - (2)$

Adding equation 1 and 2, We get.

$\tt - x + y = 2. \\ \tt 2x - y = 1. \\ - - - - - - - - \\ \tt \implies x = 3.$

Now, Putting the value x = 3 in equation 1, we get.

$\tt\implies 2x - y = 1. \\ \tt \implies2(3) - y = 1 \\ \tt \implies- y = - 5. \\ \tt\implies y = 5.$

So,

• Ten place number be 3.
• and Unit place be 5.

then,

$\longrightarrow 10x + y \\ \tt\longrightarrow 10(x )+ (y). \\ \tt\longrightarrow 10(3) + 5. \\ \tt\longrightarrow35.$

Therefore, the required number be 35.